Abstract
Two classes of methods for numerical integration are presented : The class of Newton-Cotes methods and the class of Gauss methods. In the class of Newton-Cotes methods, the trapezoidal rule, Simpson's rule and other higher order rules like Romberg's method have been derived . The methods are clarified by examples. Mathematica modules are designed to derive Newton Cotes methods of any accuracy and to apply them for evaluation of integrals. Gauss methods are derived in general form with n Gauss-Legendres knots and in particular with n=1,2,3,4 knots. Example illustrating the methods are presented. The exact analysis of both methods of numerical integration has been carrying out. A set of questions is enclosed in the chapter.
Keywords: Newtons-Cotes formulas, Gauss formulas.
Related Books
Boundary Element Methods for Heat Transfer with Phase Change Problems: Theory and Application
Advanced Calculus - Fundamentals of Mathematics
Advanced Numerical Methods for Complex Environmental Models: Needs and Availability
An Introduction to Sobolev Spaces
An Introduction to Trigonometry and its Applications
Analysis and Optimal Control of Phase-Field Transition System: Fractional Steps Methods
Applied Computational Mathematics in Social Sciences
Calculus: The Logical Extension of Arithmetic
Complex Analyses in Engineering, Science and Technology
Convergence Theorems for Lattice Group-Valued Measures